Playing With Numbers

A boy multiplied $$987$$ by a certain number and obtained $$559981$$ as his answer. If in the answer both $$9$$ are wrong and the other digits are correct, then the correct answer would be:
When a natural number $$n$$ is divided by $$4$$, the remainder is $$3$$. What is the remainder when $$2n$$ is divided by $$4$$?
Consider the following statements:
A number $${ a }_{ 1 }{ a }_{ 2 }{ a }_{ 3 }{ a }_{ 4 }{ a }_{ 5 }$$ is divisible by $$9$$ if
1. $${ a }_{ 1 }+{ a }_{ 2 }+{ a }_{ 3 }+{ a }_{ 4 }+{ a }_{ 5 }$$ is divisible by $$9$$.
2. $${ a }_{ 1 }-{ a }_{ 2 }+{ a }_{ 3 }-{ a }_{ 4 }+{ a }_{ 5 }$$ is divisible by $$9$$.
Which of the above statements is/are correct?
Using divisibility tests, determine which of the following numbers are divisible by $$10$$:
(a) $$54450$$ (b) $$10800$$ (c) $$7138965$$ (d) $$7016930$$ (e) $$10101010$$
$$24 P$$ leaves remainder $$1$$ if it is divided by $$3$$ and leaves remainder $$2$$ if it is divided by $$5$$. 
Find the value of $$P$$